Looking at the position I guessed that playing Ka2 as a preparatory move would be an idea to avoid a check, but when?

The winning idea is to play it after 2. Be3! Amazingly, Black is in virtual Zugzwang.

The setter Carel Mann is worth a post on his own,

http://web.inter.nl.net/hcc/rekius/mann.htm

Carel Mann (1871-1928) was born in Amsterdam, as the son of a butcher. He got his own butcher’s shop in Haarlem at the beginning of the twentieth century. According to an anecdote, he used to compose with meat balls on the black and white tiles of his shop. A small inheritance of his mother allowed him to stop his trade and live the life of a poor tramp. He became mentally ill, suffering from paranoid schizophrenia. His illusion was a vampire, who sucked his red blood cells at night. At daytime the vampire had the image of a human being. Mann ‘recognised’ his enemy on the boat from Marseilles to Algiers and fired a revolver. Fortunately he missed. He was sentenced to receive mental treatment, and went to an institution in Ermelo. Patients were locked up inside. Outside they were chained. When he moved to Geel, his treatment became more humane. After his flight, no measures were taken. He started to compose endgame studies in Amsterdam. King chases became the main theme.

Mann’s obsession with king chases could have been based on paranoia. In the Freudian version, the naughty black man(n) is chased by the white queen and her helper to every corner of the board. Counter-play is hardly possible. On the forced way to the fatal end, an occasional quiet move underlines fate. However, fear of women was not his obsession. Some paranoia is usual for a chess player, because of the illusion that the opponent wants to hurt you. Mann illustrated the paranoia of chess.

If Be3 mate on g1 can only be avoided by either Kh2 or Qh2 which loses after Qf3 Qd1 Bf4.

So after Kh2, Ka2! Then we get the threat Bf4+ Qf3 without allowing Qg7+ Qf7. If Qf7 after Ka2 then Bf4 Qh3 Be3 wins the BQ.

After trying every move, the only move that doesn't lose on the spot is b6! Can you see what he did there? Then a similar variation to Richard's takes place - makes use of vacated a1 and no Qe5+ by black at the end.

...is not the solution! Although it does raise the same question that we had with the 1908, of an alternative variation that doesn't look entirely unresolved. To wit, although I don't think White is winning at the end of your line, I'm not at all sure I can prove it.

We'll maybe get back to that, beginning perhaps with 11..Kg2. But as it stands, there's something rather simpler that you've not quite got!

(By the way, readers thinking 'wasn't there another comment in there earlier?' are not deluded, I'd commented to the effect that the 1910 was still unsolved, which wasn't right. I meant the 1909, which has now been solved anyway.)

Is it a coincidence then that both 1908 and 1912 were provided by Sean?!

This Anon has nothing to add to the Mann study (except that he hopes to see the real solution soon!). No, he just wants to record his thanks to EJH for another fine set of 14(!) Xmas puzzles. Roll on December 25 2012. Sixteen puzzles this time with two cooks to find, perhaps?

I haven't yet seen the refutation of 3. ... d2 - it seems that White needs a precise sequence of checks before Black's queen swoops in on c2 and/or Black's pawn promotes on d1.

Assuming there IS a refutation of 3. ... d2, then we can concur that 3. ... b6 is the only move and we probably need to find a cunning sequence to "triangulate" and pass the move back to Black again. Or is it even easier than that?